In Defense of the Humble Local Maximum

Samuel Hulick |
April 14, 2016

When I first came across the concept of a “local maximum,” it blew my freaking mind.

Here’s the general gist:

Imagine it’s a pitch-black, foggy night and you’re airdropped into a random spot in a hilly terrain. Your mission is to hike up as high up as possible, but your lantern only lets you see a few feet around you. What should you do?

The most obvious thing would be to just make sure you keep moving in an upward direction (remember you can only see a few feet around you). That way, you’re basically guaranteed to wind up at the top of whichever hill you happened to land on.

But what if it’s a really short hill and there’s another one that’s way taller? Your “always go up” strategy will get you to the top of the hill you’re currently on (the “local maximum”), but it won’t get you to the top of the tallest one (the “global maximum”).

This metaphorical conundrum is an old mathematics/compsci concept used for identifying the peak item in a given data set. The design world has recently borrowed it as a metaphor, with mixed results.

Design and the local maximum

The way a lot of people apply the hill climbing concept to design and optimization is as follows: when you initially design something, it’s like being airdropped into a random location, and optimizing it is like climbing the hill you landed on.

It’s usually used as a cautionary tale, warning that if you slavishly pursue improving metrics and nothing else, you will inevitably neglect to consider radical alternatives that may have an even higher ceiling than the thing you’re optimizing. Often, this super cool and scientific-looking illustration accompanies it:

This notion has often been used to discourage people from overcommitting to website optimization (“climbing the hill you’re on”) and instead radically redesigning things (“trying for the bigger hill”).

This is a very cool concept, but its application to design is very flawed. Here’s why.

Breakdown #1: Inky blackness and casino luck

Remember when the hill-climbing analogy started with you being randomly dropped in an unknown terrain, where you could only see a few feet around you?

This implies you have no way of knowing whether you’re on a tall or short hill to begin with. You’re surrounded by inky blackness, so it’s impossible to compare your situation to another.

Keep in mind when looking at the cool diagram above that you don’t know where the bigger hill is, or how much bigger it is, or even if there IS a bigger hill—for all you know, you might already be on the biggest hill!

Let’s fix that now. Here’s what you can actually see:

Don’t forget that in the metaphor, where you land is random. Therefore, redesigning isn’t “the bigger hill”—it’s just another chance to get airdropped onto it. You could just as easily wind up landing on a hill that’s even shorter than the one you’re on now.

Redesigning is like taking another spin on a roulette wheel, not getting to decide where the ball winds up.

Breakdown #2: Infinite possibilities = no global maximum

Another core fallacy with this analogy is that there is a “tallest” hill to begin with (i.e. the “global maximum”).

While the diagram only shows two hills, we know there are way more than just two possibilities of how a website could be designed. In fact, it’s pretty easy to claim that there are infinite possible designs for a site.

This means that the “terrain” in which you’re working is infinite, as is the number of hills it contains. And an infinite number of hills means there is no “biggest” hill. It’s all just varying degrees of “local maxima.”

In that sense, the local maximum is not a terrible place to be—it literally means you’re “maxing” out the thing you’re optimizing. Few designs achieve anything approaching that state.

Is it possible there are other design possibilities out there that could be optimized even further, however? Yep. It’s pretty much a given considering the infinite landscape we’re working in.

Sometimes blowing up what you have so you can “switch hills” is the right move, even if it’s a spin of the aforementioned roulette wheel. Still, hitting any hill’s local maximum will always be more desirable than not hitting it.

Running up against a local maximum should be a goal, not something to be scared of.

Breakdown #3: Hills stay put, websites evolve

Lastly, how are we even defining one version of a website as being distinct from another? It’s easy to see two hills as unique, unwaveringly individual objects, but the multi-faceted experience of using a digital interface? Not so much.

What if you completely revamped a site’s layout but left its architecture in place? What if you overhauled its aesthetic but kept the feature set as-is? What if you kept everything else exactly the same but added more content?

How much does a website have to change to become a metaphorical “other hill”? 70 percent? 100 percent? And what specifically has to be changed?

Glaciers and earthquakes notwithstanding, hills are fixed elements in their landscape. A website is decidedly not. Not only are websites infinitely adaptable, the landscape they reside on—the intentions of the people pulling them up—is constantly evolving, as well.

So not only is the terrain you’re “parachuting into” not finite, it’s not even standing still.

A theory of relativity

Optimizations and redesigns are not enemies. Nor are they opposites. In fact, they’re not even different things.

Any analogy that compels people to say, “See! There’s a point where you should stop optimizing and redesign instead!” is missing the boat. Optimizing is redesigning— it’s just keeping score while it’s at it.

What I think trips people up are the granularities of a design change.

Every change to a website is a “radical redesign” within that change’s scope. This is true for everything from a site’s entire architecture all the way down to the most stereotypical “tiny optimization” tweaks like changing button colors.

You do not need to stop optimizing in order to start redesigning.

Optimization literally can’t happen without redesigning something, and measuring how a redesign went doesn’t make it any less of a redesign.

Changing a button’s color and text is still a “radical redesign,” within the scope of that button. Completely overhauling every element on an entire screen in one fell swoop is still optimization, provided the new version went live in such a way that you could gauge its performance.

Breadth control

Let’s change the nature of the question from the either/or of “Should I be optimizing or redesigning?” to “What level of granularity should this design change be?”

Sometimes you will want to do spot work on a design’s details, and sometimes you will want to change its entire foundation, but the process of changing a design should always be the same, regardless of its scope.

A button can have a local maximum, just as a block of content could, or an entire screen, or an entire site. Embrace it. Pursue it, even.